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Volumn 189, Issue 1, 2004, Pages 88-147

Quantum zonal spherical functions and Macdonald polynomials

Author keywords

Macdonald polynomials; Quantum groups; Zonal spherical functions

Indexed keywords


EID: 15844376697     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aim.2003.11.007     Document Type: Article
Times cited : (35)

References (29)
  • 1
    • 84957316947 scopus 로고
    • On root systems and an infinitesimal classification of irreducible symmetric spaces
    • S. Araki, On root systems and an infinitesimal classification of irreducible symmetric spaces, J. Math. Osaka City Univ. 13 (1) (1962) 1-34.
    • (1962) J. Math. Osaka City Univ. , vol.13 , Issue.1 , pp. 1-34
    • Araki, S.1
  • 3
    • 22044453536 scopus 로고    scopus 로고
    • A family of quantum projective spaces and related q-hypergeometric orthogonal polynomials
    • M.S. Dijkhuizen, M. Noumi, A family of quantum projective spaces and related q-hypergeometric orthogonal polynomials, Trans. AMS 350 (8) (1998) 3269-3296.
    • (1998) Trans. AMS , vol.350 , Issue.8 , pp. 3269-3296
    • Dijkhuizen, M.S.1    Noumi, M.2
  • 4
    • 0242318910 scopus 로고    scopus 로고
    • Some limit transitions between BC type orthogonal polynomials interpreted on quantum complex Grassmannians
    • M.S. Dikhhuizen, J.V. Stokman, Some limit transitions between BC type orthogonal polynomials interpreted on quantum complex Grassmannians, Publ. Res. Inst. Math. Sci. 35 (1999) 451-500.
    • (1999) Publ. Res. Inst. Math. Sci. , vol.35 , pp. 451-500
    • Dikhhuizen, M.S.1    Stokman, J.V.2
  • 5
    • 0007278034 scopus 로고
    • Fundamental solutions of invariant differential operators on symmetric spaces
    • S. Helgason, Fundamental solutions of invariant differential operators on symmetric spaces, Amer. J. Math. 86 (1964) 565-601.
    • (1964) Amer. J. Math. , vol.86 , pp. 565-601
    • Helgason, S.1
  • 9
    • 0031116634 scopus 로고    scopus 로고
    • On a Harish-Chandra homomorphism
    • A. Joseph, On a Harish-Chandra homomorphism, C. R. Acad. Sci. Paris Ser. I Math. 324 (7) (1997) 759-764.
    • (1997) C. R. Acad. Sci. Paris Ser. I Math. , vol.324 , Issue.7 , pp. 759-764
    • Joseph, A.1
  • 10
    • 0033116499 scopus 로고    scopus 로고
    • A completion of the quantized enveloping algebra of a Kac-Moody algebra
    • A. Joseph, A completion of the quantized enveloping algebra of a Kac-Moody algebra, J. Algebra 214 (1) (1999) 235-275.
    • (1999) J. Algebra , vol.214 , Issue.1 , pp. 235-275
    • Joseph, A.1
  • 11
    • 0000332410 scopus 로고
    • Local finiteness of the adjoint action for quantized enveloping algebras
    • A. Joseph, G. Letzter, Local finiteness of the adjoint action for quantized enveloping algebras, J. Algebra 153 (1992) 289-318.
    • (1992) J. Algebra , vol.153 , pp. 289-318
    • Joseph, A.1    Letzter, G.2
  • 12
    • 0000878530 scopus 로고
    • Separation of variables for quantized enveloping algebras
    • A. Joseph, G. Letzter, Separation of variables for quantized enveloping algebras, Amer. J. Math. 116 (1994) 127-177.
    • (1994) Amer. J. Math. , vol.116 , pp. 127-177
    • Joseph, A.1    Letzter, G.2
  • 13
    • 0036331133 scopus 로고    scopus 로고
    • Evaluation of the quantum affine PRV determinants
    • A. Joseph, G. Letzter, Evaluation of the quantum affine PRV determinants, Math. Res. Lett. 9 (2002) 307-322.
    • (2002) Math. Res. Lett. , vol.9 , pp. 307-322
    • Joseph, A.1    Letzter, G.2
  • 14
    • 0009464049 scopus 로고
    • Askey-Wilson polynomials as zonal spherical functions on the SU(2) quantum group
    • T.H. Koornwinder, Askey-Wilson polynomials as zonal spherical functions on the SU(2) quantum group, SIAM J. Math. Anal. 24 (3) (1993) 795-813.
    • (1993) SIAM J. Math. Anal. , vol.24 , Issue.3 , pp. 795-813
    • Koornwinder, T.H.1
  • 15
    • 0000515270 scopus 로고
    • Askey-Wilson polynomials for root systems of type BC
    • Hypergeometric functions on domains of positivity, Jack polynomials and applications
    • T.H. Koornwinder, Askey-Wilson polynomials for root systems of type BC, in: Hypergeometric functions on domains of positivity, Jack polynomials and applications, Contemp. Math. 138 (1992) 189-204.
    • (1992) Contemp. Math. , vol.138 , pp. 189-204
    • Koornwinder, T.H.1
  • 17
    • 0031490755 scopus 로고    scopus 로고
    • Lectures on affine Hecke algebras and Macdonald's conjectures
    • A.A. Kirillov Jr., Lectures on affine Hecke algebras and Macdonald's conjectures, Bull. AMS, New Ser. 34 (3) (1997) 251-292.
    • (1997) Bull. AMS, New Ser. , vol.34 , Issue.3 , pp. 251-292
    • Kirillov Jr., A.A.1
  • 18
    • 0031352797 scopus 로고    scopus 로고
    • Subalgebras which appear in quantum Iwasawa decompositions
    • G. Letzter, Subalgebras which appear in quantum Iwasawa decompositions, Canad. J. Math. 49 (6) (1997) 1206-1223.
    • (1997) Canad. J. Math. , vol.49 , Issue.6 , pp. 1206-1223
    • Letzter, G.1
  • 19
    • 0033569267 scopus 로고    scopus 로고
    • Symmetric pairs for quantized enveloping algebras
    • G. Letzter, Symmetric pairs for quantized enveloping algebras, J. Algebra 220 (2) (1999) 729-767.
    • (1999) J. Algebra , vol.220 , Issue.2 , pp. 729-767
    • Letzter, G.1
  • 20
    • 0141974009 scopus 로고    scopus 로고
    • Coideal subalgebras and quantum symmetric pairs
    • MSRI publications, Cambridge University Press, Cambridge
    • G. Letzter, Coideal subalgebras and quantum symmetric pairs, in: New Directions in Hopf Algebras, MSRI publications, Vol. 43, Cambridge University Press, Cambridge, 2002, pp. 117-166.
    • (2002) New Directions in Hopf Algebras , vol.43 , pp. 117-166
    • Letzter, G.1
  • 21
    • 0141888427 scopus 로고    scopus 로고
    • Quantum symmetric pairs and their zonal spherical functions
    • G. Letzter, Quantum symmetric pairs and their zonal spherical functions, Transformation Groups 8 (3) (2003) 261-292.
    • (2003) Transformation Groups , vol.8 , Issue.3 , pp. 261-292
    • Letzter, G.1
  • 22
    • 0004132326 scopus 로고
    • Spherical functions on a group of p-adic type
    • Publications of the Ramanujan Institute, Ramanujan Institute, Center for Advanced Study in Mathematics, University of Madras, Madras
    • I.G. Macdonald, Spherical functions on a group of p adic type, Publications of the Ramanujan Institute, Vol. 2, Ramanujan Institute, Center for Advanced Study in Mathematics, University of Madras, Madras, 1971.
    • (1971) , vol.2
    • Macdonald, I.G.1
  • 23
    • 0742316538 scopus 로고    scopus 로고
    • Orthogonal polynomials associated with root systems
    • I.G. Macdonald, Orthogonal polynomials associated with root systems, Sém. Lotharingien Combin. 45 (2000/01) 40.
    • (2000) Sém. Lotharingien Combin. , vol.45 , pp. 40
    • Macdonald, I.G.1
  • 24
    • 0030588041 scopus 로고    scopus 로고
    • Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces
    • M. Noumi, Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces, Adv. Math. 123 (1) (1996) 16-77.
    • (1996) Adv. Math. , vol.123 , Issue.1 , pp. 16-77
    • Noumi, M.1
  • 25
    • 0142008657 scopus 로고    scopus 로고
    • Multivariable Askey-Wilson polynomials and quantum complex Grassmannians
    • M. Noumni, M.S. Dijkhuizen, T. Sugitani, Multivariable Askey-Wilson polynomials and quantum complex Grassmannians, Fields Inst. Commun. 14 (1997) 167-177.
    • (1997) Fields Inst. Commun. , vol.14 , pp. 167-177
    • Noumni, M.1    Dijkhuizen, M.S.2    Sugitani, T.3
  • 26
    • 0002047632 scopus 로고
    • Quantum symmetric spaces and related q-orthogonal polynomials
    • Toyonaka, Japan, 1994, World Science Publishing, River Edge, NJ
    • M. Noumi, T. Sugitani, Quantum symmetric spaces and related q-orthogonal polynomials, in: Group Theoretical Methods in Physics (ICGTMP), Toyonaka, Japan, 1994, World Science Publishing, River Edge, NJ, 1995, pp. 28-40.
    • (1995) Group Theoretical Methods in Physics (ICGTMP) , pp. 28-40
    • Noumi, M.1    Sugitani, T.2
  • 28
    • 0142008656 scopus 로고    scopus 로고
    • Zonal spherical functions on quantum Grassmann manifolds
    • T. Sugitani, Zonal spherical functions on quantum Grassmann manifolds, J. Math. Sci. Univ. Tokyo 6 (2) (1999) 335-369.
    • (1999) J. Math. Sci. Univ. Tokyo , vol.6 , Issue.2 , pp. 335-369
    • Sugitani, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.